Why are Indifference Curves always downwards sloping?Please explain with a graph and diagram and equation if possible

If a consumer equally prefers two product bundles, then the consumer is indifferent between the two bundles. The consumer will get the same level of satisfaction (utility) from either bundles. The slope of indifference curve is the rate at which a consumer is willing to trade one good for another, which is also known as the marginal rate of substitution (MRS).

Indifference curves are downward sloping. If the quantity of one goods is reduced, then you must have more of the other good to compensate for the loss.

Indifference curves are bowed inward (in most cases). The slope of indifference curves represent the MRS (rate at which consumers are willing to substitute one good for the other). People are usually willing to trade away more of one good when they have a lot of it, and less willingto trade away goods which are in scarce supply. This implies that MRS must increase as we get less of a good.

The marginal rate of substitution (MRS) is the slope of the indifference curve. It is derived mathematically for a non-linear indifference curve by taking the constant slope of the straight-line tangent to the curve at the particular point of interest. Intuitively, the absolute value of the MRS is the ratio between the marginal amount of good y that must be given to compensate for a marginal loss of good x, and the marginal loss of good x. The higher is the marginal utility of good x, the more utility is lost when good x is taken away. The lower the marginal utility of good y, the moreof it must be given to compensate for a given utility loss. Hence it is also intuitive that the MRS is the ratio -MUx/MUy. The MRS changes along a non-linear indifference curve. For the downward-sloping convex indifference curves which result from well-behaved preferences, the MRS is always negative, and always decreases (becomes greater in absolute value) as the amount of good x decreases.

An indifference curve shows the combination of two products that provide an individual with a given level of utility (satisfaction).

Assuming the products are "good" (i.e. we want more of them rather than less) then if we have more of one product we must give up some of the other to compensate and still maintain the same total utility; therefore an indifference curve must slope downwards from left to right from quadrant 1 to 3 on the diagram. No combination in quadrant 2 could be on the same indifference curve as combination X because it would have more of product A and product B and would therefore have a higher utility. No combination of products in quadrant 4 could be on the same indifference curve as combination X because it would have less of product A and B and would therefore have lower utility.